The book 6

A boy read 3/8th of a book on one day and 4/5th of the remainder on another day . If there were 30 pages unread, how many pages did the book contain?

Final Answer:

n =  240

Step-by-step explanation:

$$\begin{gathered} a=\frac{3}{8}=0.375 \\ b=\frac{4}{5}\cdot (1-a)=\frac{4}{5}\cdot (1-\frac{3}{8})=\frac{1}{2}=0.5 \\ r=a+b=\frac{3}{8}+\frac{1}{2}=\frac{3}{8}+\frac{4}{8}=\frac{3+4}{8}=\frac{7}{8}=0.875 \\ R=1-r=1-\frac{7}{8}=\frac{1\cdot 8}{8}-\frac{7}{8}=\frac{8}{8}-\frac{7}{8}=\frac{8-7}{8}=\frac{1}{8}=0.125 \\ R\cdot n=30 \\ n=30/R=30/\frac{1}{8}=30:\frac{1}{8}=30\cdot \frac{8}{1}=\frac{30\cdot 8}{1}=\frac{240}{1}=240 \end{gathered}$$

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